Solved: A run is a maximal sequence of successes in a
Chapter 6, Problem 6.4.21(choose chapter or problem)
A run is a maximal sequence of successes in a sequence of Bernoulli trials. For example, in the sequence S. S, S, F, S, S, F, F, S, where S represents success and F represents failure, there are three runs consisting of three successes, two successes, and one success, respec" tively. Let R denote the random variable on the set of sequences of n independent Bernoulli trials that counts the number of runs in this sequence. Find E(R). [Hint: Show that R = L=I lj, where lj = I if a run begins at the jth Bernoulli trial and lj = 0 otherwise. Find E(lJ) and then find E(lj), where I < j :'S n.]
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